Concepts6

Fast I/O reduces overhead from C and C++ stream synchronization and avoids unnecessary flushes, which can cut runtime by multiples on large inputs.

Bitset optimization exploits word-level parallelism so one CPU instruction processes 64 bits at once on typical 64-bit machines.

Sum over Subsets (SOS) DP lets you compute F[mask] = sum of A[submask] over all submasks in O(n 2^n) instead of O(3^n).

Bitmask DP compresses the state of a subset of n elements into an integer mask, enabling elegant dynamic programming over all subsets.

Bitmask DP subset enumeration lets you iterate all submasks of a given mask using the idiom for (s = mask; s > 0; s = (s - 1) & mask).

Dynamic Programming (DP) state design is the art of choosing what information to remember so that optimal substructure can be reused efficiently.